{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 800x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "# 加载数据集\n",
    "iris = datasets.load_iris()\n",
    "# 拿到特征\n",
    "X = iris.data\n",
    "# 拿到目标值\n",
    "y = iris.target\n",
    "\n",
    "# 选择前两个特征进行可视化\n",
    "X_vis = X[:, :2]\n",
    "\n",
    "# 划分训练集和测试集（这里我们只用训练集进行可视化）\n",
    "X_train, _, y_train, _ = train_test_split(X_vis, y, test_size=0.3, random_state=42)\n",
    "\n",
    "# 数据标准化\n",
    "scaler = StandardScaler()\n",
    "X_train_scaled = scaler.fit_transform(X_train)\n",
    "\n",
    "# 训练SVM模型（这里以RBF核为例）\n",
    "svm_rbf = SVC(kernel='rbf', C=1)\n",
    "svm_rbf.fit(X_train_scaled, y_train)\n",
    "\n",
    "# 使用训练好的模型对训练数据进行预测（仅为了可视化）\n",
    "y_pred = svm_rbf.predict(X_train_scaled)\n",
    "\n",
    "# 可视化\n",
    "plt.figure(figsize=(8, 6))\n",
    "colors = ['red', 'green', 'blue']\n",
    "for i in range(3):\n",
    "    # 绘制每个类别的点\n",
    "    plt.scatter(X_train_scaled[y_train == i, 0], X_train_scaled[y_train == i, 1],\n",
    "                c=colors[i], label=iris.target_names[i])\n",
    "\n",
    "# 这里我们不直接绘制决策边界，因为它在标准化后的空间中，但可以绘制预测结果的点\n",
    "# 如果你想要绘制决策边界，你需要找到一种方法来在原始特征空间或二维投影中近似它\n",
    "\n",
    "# 添加图例\n",
    "plt.legend()\n",
    "# 添加标题和坐标轴标签\n",
    "plt.title('Iris Classification with SVM (RBF Kernel)')\n",
    "plt.xlabel('Sepal length (scaled)')\n",
    "plt.ylabel('Sepal width (scaled)')\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  },
  {
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    "X_train_scaled\n"
   ],
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   "execution_count": 9,
   "outputs": [
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     "execution_count": 9,
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     "output_type": "execute_result"
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